Testing Evolutionary Theories of Aging and

Longevity

Dr. Natalia S. Gavrilova, Ph.D.Dr. Leonid A. Gavrilov, Ph.D.

Center on Aging

NORC and The University of Chicago Chicago, Illinois, USA

What are the data and the predictions of evolutionary

theories of aging on

Variability of age-related outcomes

Old-age mortality trajectories

Trade-offs between longevity and fertility

Part 1 Testing Predictions of Programmed vs. Stochastic

Aging Opponents of programmed aging often

argue that there is a too high variation in timing of aging-related outcomes, compared to much smaller variation in timing of programmed developmental outcomes (such as age of sexual maturation).

In other words, aging just does not have an expected clock-wise accuracy, which is anticipated for programmed events.

Part 1 Testing Predictions of Programmed vs. Stochastic

Aging To test the validity of this argument we compared

relative variability (coefficient of variation) for parameters that are known to be determined by the developmental program (age at sexual maturity) with variability of characteristic related to aging (age at menopause).

We used information on the ages at sexual maturation (menarche) and menopause from the nationally representative survey of the adult population of the United States (MIDUS) as well as published data for 14 countries.

Why use relative variability, coefficient of

variation? "The fact that elephants, for instance, may have a standard

deviation of 50 mm for some linear dimension and shrews a standard deviation of 0.5 mm for the same dimension does not necessarily mean that the elephants are more variable, in the essential zoological sense, than the shrews. The elephants are a hundred times the size of the shrews in any case, and we should expect the absolute variation also to be a hundred times as great without any essential difference in functional variability. The solution of this problem is very simple: it is necessary only to relate the measure of absolute variation to a measure of absolute size. The best measures to use for this purpose are the standard deviation and the mean, and since their quotient is always a very small number it is convenient to multiply it by 100. The resulting figure is a coefficient of variation, or of variability"Simpson GG, Roe A, Lewontin RG. Quantitative Zoology:

Revised Edition. New York: Dover Publications, Inc.; 2003.

Our results using the MIDUS study

National survey conducted in 1994/95

Americans aged 25-74 core national sample (N=3,485) city oversamples (N=957)

Additional samples: twins, siblings

Subsample used in this study: women having natural menopause (no surgeries affecting the age at menopause) aged 60-74

A 30-40 minute telephone survey A 114 page mail survey

Number of respondents: 4,242 Number of respondents: 3,690

Women Aged 25-74 (n=2,087)AGE 25-54 68.8 55-64 19.8 65-74 11.4RACE/ETHNICITY White 86.9 African-American 7.7 Other 8.9RELATIONSHIP STATUS Married 54.2 Other intimate relationship 4.7

MIDUS SAMPLE POPULATION

DISTRIBUTIONS (%)

DISTRIBUTION OF AGE AT MENARCHE IN THE MIDUS SAMPLE

DISTRIBUTION OF AGE AT MENOPAUSE IN THE MIDUS

SAMPLE

Variation for characteristics of human aging and development

Characteristic Mean age (SD) years

Coefficient of variation

Source

Age at onset of menarche

12.9 (1.6) 12.4% MIDUS data

Age at onset of menopause

49.7 (5.2) 10.5% MIDUS data

Age at death 78.7 (16.1)

20.5% USA, women, 1995. Human mortality database

Variation of age at onset of menarche and age at death (in

2005)

Country Mean age (SD) for onset of

menarche

CV%

Mean age (SD) at death

CV%

France 12.84 (1.40) 10.9 83.3 (13.8)

16.6

Italy 12.54 (1.46) 11.6 83.3 (13.1)

15.7

Sweden 13.59 (1.41) 10.4 82.3 (12.9)

15.7

UK 12.89 (1.54) 12.0 80.2 (14.0)

17.5

USA 12.9 (1.60) 12.4 78.7 (16.1)

20.5

Mean age (standard deviation, SD) at natural menopause

Population Mean age (SD) at menopause,

years

Source

South Korean women

46.9 (4.9) Hong et al., MATURITAS, 2007

Viennese women aged 47 to 68

49.2 (3.6) Kirchengast et al., International Journal of Anthropology , 1999

Mexico: Puebla Mexico city

46.7 (4.77)46.5 (5.00)

Sievert, Hautaniemi, Human Biology, 2003

Black women in South Africa: rural urban

49.5 (4.7)48.9 (4.2)

Walker et al., International Journal of Obstetrics & Gynaecology, 2005

Mean Values and Standard Deviations for Human Developmental

Characteristics

Comparison of mean ages at menarche (1), menopause (2), and death (3) as well as their standard deviations for studied human populations. Source: Gavrilova N.S., Gavrilov L.A., Severin, F.F. and Skulachev, V.P. Testing predictions of the programmed and stochastic theories of aging: Comparison of variation in age at death, menopause, and sexual maturation. Biochemistry (Moscow), 2012, 77(7), 754-760.

Conclusions

Relative variability, coefficients of variation, for ages at onset of menarche and ages at death for contemporary populations are of the same order of magnitude

Theories of programmed aging are fruitful in suggesting new testable predictions.

"Although any claim that humans are programmed to age and die would be highly speculative, we believe that as a hypothesis it suggests fruitful avenues for biological and even medical research." Longo VD, Mitteldorf J, Skulachev VP. Programmed and altruistic ageing. Nature Review Genetics. 2005 Nov;6(11): 866-72.

To read more about this part of our study see:

Gavrilova NS, Gavrilov LA, Severin FF, Skulachev VP. Testing predictions of the programmed and stochastic theories of aging: comparison of variation in age at death, menopause, and sexual maturation. Biochemistry (Moscow). 2012 Jul;77(7):754-60. http://www.ncbi.nlm.nih.gov/pubmed/22817539

Part 2 Testing the Prediction of Late-Life

Mortality Plateau Many evolutionary biologists believe that aging

can be readily understood in terms of the declining force of selection pressure with age.

At extremely old postreproductive ages when the force of natural selection reaches a zero plateau, some evolutionary biologists (i.e. Michael Rose) believe that the mortality plateau should also be observed (no further increase in mortality rates with age).

To test the validity of this argument we analyzed mortality data for humans, rats and mice.

Some evolutionary theories predict late-life mortality

plateau

Source: Presentation by Michael Rose

When the force of natural selection reaches a zero plateau, the

mortality plateau is also expected

Problems with Hazard Rate Estimation

At Extremely Old Ages

1. Mortality deceleration in humans may be an artifact of mixing different birth cohorts with different mortality (heterogeneity effect)

2. Standard assumptions of hazard rate estimates may be invalid when risk of death is extremely high

3. Ages of very old people may be highly exaggerated

Monthly Estimates of Mortality are More Accurate

Simulation assuming Gompertz law for hazard rate

Stata package uses the Nelson-Aalen estimate of hazard rate:

H(x) is a cumulative hazard function, dx is the number of deaths occurring at time x and nx is the number at risk at time x before the occurrence of the deaths. This method is equivalent to calculation of probabilities of death:

q x =d x

l x

x = H( )x H( )x 1 =

d x

n x

Social Security Administration’s Death Master File (SSA’s DMF) Helps to Alleviate the First Two

Problems

Allows to study mortality in large, more homogeneous single-year or even single-month birth cohorts

Allows to estimate mortality in one-month age intervals narrowing the interval of hazard rates estimation

What Is SSA’s DMF ?

As a result of a court case under the Freedom of Information Act, SSA is required to release its death information to the public. SSA’s DMF contains the complete and official SSA database extract, as well as updates to the full file of persons reported to SSA as being deceased.

SSA DMF is no longer a publicly available data resource (now is available from Ancestry.com for fee)

We used DMF full file obtained from the National Technical Information Service (NTIS). Last deaths occurred in September 2011.

SSA DMF birth cohort mortality

Nelson-Aalen monthly estimates of hazard rates using Stata 11

Conclusions from our earlier study of SSA DMF

Mortality deceleration at advanced ages among DMF cohorts is more expressed for data of lower quality

Mortality data beyond ages 106-107 years have unacceptably poor quality (as shown using female-to-male ratio test). The study by other authors also showed that beyond age 110 years the age of individuals in DMF cohorts can be validated for less than 30% cases (Young et al., 2010)

Source: Gavrilov, Gavrilova, North American Actuarial Journal, 2011, 15(3):432-447

Selection of competing mortality models using DMF

data Data with reasonably good quality were

used: non-Southern states and 85-106 years age interval

Gompertz and logistic (Kannisto) models were compared

Nonlinear regression model for parameter estimates (Stata 11)

Model goodness-of-fit was estimated using AIC and BIC

Fitting mortality with Kannisto and Gompertz models

Kannisto model

Gompertz model

Akaike information criterion (AIC) to compare Kannisto and Gompertz

models, men, by birth cohort (non-Southern states)

Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval 85-106 years

U.S. Males

-370000

-350000

-330000

-310000

-290000

-270000

-250000

1890 1891 1892 1893 1894 1895 1896 1897 1898 1899

Birth Cohort

Aka

ike

crit

erio

nGompertz Kannisto

Akaike information criterion (AIC) to compare Kannisto and Gompertz models, women, by

birth cohort (non-Southern states)

Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval 85-106 years

U.S. Females

-900000

-850000

-800000

-750000

-700000

-650000

-600000

1890 1891 1892 1893 1894 1895 1896 1897 1898 1899

Birth Cohort

Akaik

e C

rite

rio

n

Gompertz Kannisto

The second studied dataset:U.S. cohort death rates taken

from the Human Mortality Database

Selection of competing mortality models using HMD

data Data with reasonably good quality were

used: 80-106 years age interval Gompertz and logistic (Kannisto) models

were compared Nonlinear weighted regression model for

parameter estimates (Stata 11) Age-specific exposure values were used as

weights (Muller at al., Biometrika, 1997) Model goodness-of-fit was estimated using

AIC and BIC

Fitting mortality with Kannisto and Gompertz models, HMD U.S. data

Fitting mortality with Kannisto and Gompertz models, HMD U.S. data

Akaike information criterion (AIC) to compare Kannisto and Gompertz

models, men, by birth cohort (HMD U.S. data)

Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval 80-106 years

U.S.Males

-250

-230

-210

-190

-170

-150

1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900

Birth Cohort

Aka

ike

Cri

teri

on

Gompertz Kannisto

Akaike information criterion (AIC) to compare Kannisto and Gompertz

models, women, by birth cohort (HMD U.S. data)

Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval 80-106 years

U.S. Females

-250-240-230-220-210-200

-190-180-170-160-150

1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900

Birth Cohort

Akaik

e C

rite

rio

n

Gompertz Kannisto

Compare DMF and HMD data Females, 1898 birth cohort

Hypothesis about two-stage Gompertz model is not supported by real data

Age, years

60 70 80 90 100 110

log

Haz

ard

rate

0.01

0.1

1

DMFHMD

What about other mammals?

Mortality data for mice: Data from the NIH Interventions Testing

Program, courtesy of Richard Miller (U of Michigan)

Argonne National Laboratory data, courtesy of Bruce Carnes (U of Oklahoma)

Mortality of mice (log scale) Data by Richard Miller

Actuarial estimate of hazard rate with 10-day age intervals

males females

Bayesian information criterion (BIC) to compare the Gompertz and Kannisto

models, mice data

Dataset Miller dataControls

Miller dataExp., no life extension

Carnes dataEarly controls

Carnes dataLate controls

Sex M F M F M F M F

Cohort size at age one year

1281 1104 2181 1911 364 431 487 510

Gompertz -597.5

-496.4

-660.4 -580.6 -585.0 -566.3 -639.5

-549.6

Kannisto -565.6 -495.4 -571.3 -577.2 -556.3 -558.4 -638.7 -548.0

Better fit (lower BIC) is highlighted in red

Conclusion: In all cases Gompertz model demonstrates better fit than Kannisto model for mortality of mice after one year of age

Laboratory rats

Data sources: Dunning, Curtis (1946); Weisner, Sheard (1935), Schlettwein-Gsell (1970)

Mortality of Wistar rats

Actuarial estimate of hazard rate with 50-day age intervals Data source: Weisner, Sheard, 1935

males females

Bayesian information criterion (BIC) to compare Gompertz and Kannisto models, rat data

Line Wistar (1935)

Wistar (1970)

Copenhagen Fisher Backcrosses

Sex M F M F M F M F M F

Cohort size

1372 1407 1372 2035 1328 1474 1076 2030 585 672

Gompertz

-34.3 -10.9 -34.3 -53.7 -11.8 -46.3 -17.0 -13.5 -18.4 -38.6

Kannisto 7.5 5.6 7.5 1.6 2.3 -3.7 6.9 9.4 2.48 -2.75

Better fit (lower BIC) is highlighted in red

Conclusion: In all cases Gompertz model demonstrates better fit than Kannisto model for mortality of laboratory rats

Simulation study of the Gompertz mortality

Kernel smoothing of hazard rates .2

.4.6

.8H

azar

d, lo

g sc

ale

80 90 100 110 120age

Smoothed hazard estimate

Recent developments “none of the

age-specific mortality relationships in our nonhuman primate analyses demonstrated the type of leveling off that has been shown in human and fly data sets”

Bronikowski et al., Science, 2011

"

Conclusions for Part 2 of our Study

We found that mortality rates increase exponentially with age (the Gompertz law), and no expected late-life mortality plateaus are observed in humans, mice, and rats.

Late-life mortality deceleration and mortality plateau observed in some earlier studies may be related to problems with data quality and biased estimates of hazard rates at extreme old ages

It seems unreasonable to explain aging (Gompertz law of mortality) by declining force of natural selection, because aging continues at the same pace at extremely old postreproductive ages when the force of natural selection already reaches a zero plateau

To read more about this part of our study see:

Gavrilov L.A., Gavrilova N.S. Mortality measurement at advanced ages: A study of the Social Security Administration Death Master File. North American Actuarial Journal, 2011, 15(3): 432-447.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3269912/

Part 3 Testing the Prediction of a Trade-off between Longevity and

Fertility One of the predictions of the

disposable soma theory and the antagonistic pleiotropy theory is that exceptional longevity should come with the price of impaired fertility (longevity-fertility trade-off ).

This prediction seems to be confirmed by a high profile study published by Nature, which claimed that almost half of long lived women were childless.

Here we re-evaluate this study with more complete data

Study that Found a Trade-Off Between Reproductive Success and

Postreproductive Longevity

Westendorp RGJ, Kirkwood TBL. 1998. Human longevity at the cost of reproductive success. Nature 396: 743-746.

Extensive media coverage including BBC and over 100 citations in scientific literature as an established scientific fact. Previous studies were not quoted and discussed in this article.

Point estimates of progeny number for married aristocratic women from different birth cohorts as a

function of age at death. The estimates of progeny number are adjusted for trends over

calendar time using multiple regression.

Source: Westendorp, Kirkwood, Human longevity at the cost of reproductive success. Nature, 1998, 396, pp 743-746

“… it is not a matter of reduced fertility, but a case of 'to have or have not'.“

Table 1 Relationship between age at death and number of children for married aristocratic women

Age at death Proportion childless Number of children

(years) mean for all women mean for women having children

<20 0.66 0.45 1.32

21-30 0.39 1.35 2.21

31-40 0.26 2.05 2.77

41-50 0.31 2.01 2.91

51-60 0.28 2.4 3.33

61-70 0.33 2.36 3.52

71-80 0.31 2.64 3.83

81-90 0.45 2.08 3.78

>90 0.49 1.80 3.53

Source: Toon Ligtenberg & Henk Brand. Longevity — does family

size matter? Nature, 1998, 396, pp 743-746

Number of progeny and age at first childbirth dependent on the age at death of married aristocratic women

Source: Westendorp, R. G. J., Kirkwood, T. B. L. Human longevity at the cost of reproductive success. Nature, 1998, 396, pp 743-746

Source: Westendorp, R. G. J., Kirkwood, T. B. L. Human longevity at the cost of reproductive success. Nature, 1998, 396, pp 743-746

Do longevous women have impaired fertility ?Why is this question so important and interesting?

Scientific Significance

This is a testable prediction of some evolutionary theories of aging - disposable soma theory of aging (Kirkwood)

"The disposable soma theory on the evolution of ageing states that longevity requires investments in somatic maintenance that reduce the resources available for reproduction“ (Westendorp, Kirkwood, Nature, 1998).

Do longevous women have impaired fertility ?

Practical Importance. Do we really wish to live a long life at the cost of

infertility?: “the next generations of Homo sapiens will have even longer life

spans but at the cost of impaired fertility” Rudi Westendorp “Are we becoming less disposable?

EMBO Reports, 2004, 5: 2-6.

"... increasing longevity through genetic manipulation of the mechanisms of aging raises deep biological and moral questions. These questions should give us pause before we embark on the enterprise of extending our lives“ Walter Glennon "Extending the Human Life Span", Journal of Medicine and Philosophy, 2002, Vol. 27, No. 3, pp. 339-354.

Educational Significance Do we teach our students right?

Impaired fertility of longevous women is often presented in scientific literature and mass media as already established fact (Brandt et al., 2005; Fessler et al., 2005; Schrempf et al., 2005; Tavecchia et al., 2005; Kirkwood, 2002; Westendorp, 2002, 2004; Glennon, 2002; Perls et al., 2002, etc.).

This "fact" is now included in teaching curriculums in biology, ecology and anthropology world-wide (USA, UK,

Denmark). Is it a fact or artifact ?

General Methodological Principle:

Before making strong conclusions, consider all other possible explanations, including potential flaws in data quality and analysis

Previous analysis by Westendorp and Kirkwood was made on the assumption of data completeness:Number of children born = Number of children recorded

Potential concerns: data incompleteness, under-reporting of short-lived children, women (because of patrilineal structure of genealogical records), persons who did not marry or did not have children.Number of children born   >> Number of children recorded

Test for Data CompletenessDirect Test: Cross-checking of the initial dataset with other

data sources We examined 335 claims of childlessness in the dataset

used by Westendorp and Kirkwood. When we cross-checked these claims with other professional sources of data, we  found that at least 107 allegedly childless women (32%) did have children!

At least 32% of childlessness claims proved to be wrong ("false negative claims") !

Some illustrative examples:Henrietta Kerr (1653 1741) was apparently childless in the dataset used by Westendorp and Kirkwood and lived 88 years. Our cross-checking revealed that she did have at least one child, Sir William Scott (2nd Baronet of Thirlstane, died on October 8, 1725).

 Charlotte Primrose (1776 1864) was also considered childless in the initial dataset and lived 88 years. Our cross-checking of the data revealed that in fact she had as many as five children: Charlotte (1803 1886), Henry (1806 1889), Charles (1807 1882), Arabella (1809-1884), and William (1815 1881).

Wilhelmina Louise von Anhalt-Bernburg (1799 1882), apparently childless, lived 83 years. In reality, however, she had at least two children, Alexander (1820 1896) and Georg (1826 1902).

Point estimates of progeny number for married aristocratic women from different birth cohorts as a function of age at

death. The estimates of progeny number are adjusted for trends over calendar time using

multiple regression.

Source: Westendorp, R. G. J., Kirkwood, T. B. L. Human longevity at the cost of reproductive success. Nature, 1998, 396, pp 743-746

Antoinette de Bourbon(1493-1583)

Lived almost 90 yearsShe was claimed to have only one

child in the dataset used by Westendorp and Kirkwood: Marie (1515-1560), who became a mother of famous Queen of Scotland, Mary Stuart.

Our data cross-checking revealed that in fact Antoinette had 12 children!

Marie 1515-1560 Francois Ier 1519-1563 Louise 1521-1542 Renee 1522-1602 Charles 1524-1574 Claude 1526-1573 Louis 1527-1579 Philippe 1529-1529 Pierre 1529 Antoinette 1531-1561 Francois 1534-1563 Rene 1536-1566

Characteristics of Our Data Sample for ‘Reproduction-Longevity’ Studies

3,723 married women born in 1500-1875 and belonging to the upper European nobility.

Women with two or more marriages (5%) were excluded from the analysis in order to facilitate the interpretation of results (continuity of exposure to childbearing).

•Every case of childlessness has been checked using at least two different genealogical sources.

Childlessness is better outcome than number of children for testing

evolutionary theories of aging on human data

Applicable even for population practicing birth control (few couple are voluntarily childless)

Lifespan is not affected by physiological load of multiple pregnancies

Lifespan is not affected by economic hardship experienced by large families

Source:

Gavrilova et al. Does exceptional human longevity come with high cost of infertility? Testing the evolutionary theories of aging. Annals of the New York Academy of Sciences, 2004, 1019: 513-517.

Source: Gavrilova, Gavrilov. Human longevity and reproduction: An evolutionary perspective. In: Grandmotherhood - The Evolutionary Significance of the Second Half of Female Life. Rutgers University Press, 2005, 59-80.

Short Conclusion:

Exceptional human longevity is NOT associated with infertility or childlessness

More Detailed Conclusions We have found that previously reported high rate

of childlessness among long-lived women is an artifact of data incompleteness, caused by under-reporting of children. After data cleaning, cross-checking and supplementation the association between exceptional longevity and childlessness has disappeared.

Thus, it is important now to revise a highly publicized scientific concept of heavy reproductive costs for human longevity. and to make corrections in related teaching curriculums for students.

More Detailed Conclusions (2) It is also important to disavow the doubts and

concerns over further extension of human lifespan, that were recently cast in biomedical ethics because of gullible acceptance of the idea of harmful side effects of lifespan extension, including infertility (Glannon, 2002).

There is little doubt that the number of children can affect human longevity through complications of pregnancies and childbearing, as well as through changes in socioeconomic status,  etc.  However,  the concept of heavy infertility cost of human longevity is not supported by data, when these data are carefully reanalyzed.

Acknowledgments

This study was made possible thanks to:

generous support from the

National Institute on Aging (R01 AG028620) Stimulating working environment at the Center on Aging, NORC/University of Chicago

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